2006 AMC 12B Problem 8

Substituting $(1, 2)$ gives $$1 = \frac{2}{4} + a \quad\Rightarrow\quad a = \frac{1}{2},$$ and $$2 = \frac{1}{4} + b \quad\Rightarrow\quad b = \frac{7}{4}.$$ Therefore $$a + b = \frac{1}{2} + \frac{7}{4} = \frac{9}{4}.$$ Thus, the correct answer is E.